AnswersAlgebra III AIntroduction to Linear Functions

Introduction to Linear Functions Answers

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Red kangaroos can reach speeds up to 50 feet per second. Use the linear graph at the left to answer the questions. What is the change in y-values from Point A to Point B? ⇒ 50 What is the change in x-values from Point A to Point B? ⇒ 1 What is the rate of change of the linear function? feet per second

Answers:
⇒ 50:100
⇒ 1:2
Part 3:50
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4

What can you conclude from her work? Check all that apply.

A
The function is continuous.
B
Time represents the dependent variable.
C
The scenario is represented by a linear function, since the rate of change is constant.
D
As the amount of time continues, there are fewer cups of juice poured per hour.
E
For every additional hour, 53 cups of juice are poured.
5

Is the graphed function linear?

A
Yes, because each input value corresponds to exactly one output value.
B
Yes, because the outputs increase as the inputs increase.
C
No, because the graph is not continuous.
D
No, because the curve indicates that the rate of change is not constant.
6

Which table represents a linear function?

A
[Image: A two column table with five rows. The first colum...]
Option A
B
[Image: A two column table with five rows. The first colum...]
Option B
C
[Image: A two column table with five rows. The first colum...]
Option C
D
[Image: A two column table with five rows. The first colum...]
Option D
7

Which function has a constant additive rate of change of –1/4?

A
[Image: A coordinate plane with a straight line with a neg...]
Option A
B
[Image: A coordinate plane with a curved line passing thro...]
Option B
C
[Image: A two column table with five rows. The first colum...]
Option C
D
[Image: A two column table with five rows. The first colum...]
Option D
8

Which statement about the scenario represented in the table is true? Assume time is the independent variable.

A
The distance run is a nonlinear function because it does not have a constant rate of change.
B
The elevation is a nonlinear function because it does not have a constant rate of change.
C
Both the distance run and the elevation are nonlinear functions because they do not have constant rates of change.
D
Both the distance run and the elevation are linear functions because they have a constant rate of change.
9

The distance, in feet, two boys travel per second on a treadmill is shown to the left. Which comparison is accurate?

A
Xavier is traveling at 1.5 feet per second.
B
Moises is going faster than Xavier.
C
The difference in their rates of change is 1 foot per second.
D
If both boys remain on the treadmill for 10 minutes, Xavier will have traveled a greater distance.
10

Which best describes the data set?

A
It is nonlinear because the “Total Houses Built” column does not increase at a constant additive rate.
B
It is nonlinear because the “Months Passed” column does not increase at a constant additive rate.
C
It is nonlinear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” does not show a constant rate of change.
D
It is linear because the increase in the “Total Houses Built” compared to the increase in the “Months Passed” shows a constant rate of change.
11

Nina and Ryan each ran at a constant speed for a 100-meter race. Each runner’s distance for the same section of the race is displayed on the left. Who had a head start, and how big was the head start? had a head start of meters.

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12

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13

What is the difference between a linear function and a nonlinear function? Explain what each looks like when represented as a table and as a graph.

Answer:

A linear function has a constant additive rate of change, while a nonlinear function does not. For a table of values to be linear, the dependent variable must have a constant rate of change as the independent variable increases by 1. On a graph, the function must be a straight line to be linear.

14

What did you include in your response? Check all that apply.

A
A linear function has a constant additive rate of change.
B
A nonlinear function does not have a constant additive rate of change.
C
The graph of a linear function is a straight line, while a nonlinear graph is curved.
D
The dependent variable in a linear table has a constant additive rate of change as the independent variable increases by 1.

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